Question

Diketahui f(x) = 2x^2+5, g(x)= x-2
Tentukan (f o g)^-1(x)

Answer 1

Fog(x) = f{g(x)} = f(x-2)
fog(x) = 2(x-2)² + 5
fog(x) = 2(x²-4x+4) + 5
fog(x) = 2x²-8x + 8 + 5
fog(x)= 2x² - 8x +13
2x² -8x + 13 = y
2x²-8x = y - 13
x² - 4x = 1/2 (y-13)
(x-2)² = 1/2 (y-13) + 4
x- 2 = √{1/2(y-13) + 4}
x = 2 +- √{ 1/2(y-13) + 4}
.
(fog)⁻¹(x) = 2 +- √{¹/₂(x-13)+4}